How to execute AngularJS controller function on page load?

On the one hand as @Mark-Rajcok said you can just get away with private inner function:

// at the bottom of your controller
var init = function () {
   // check if there is query in url
   // and fire search in case its value is not empty
};
// and fire it after definition
init();

Also you can take a look at ng-init directive. Implementation will be much like:

// register controller in html
<div data-ng-controller="myCtrl" data-ng-init="init()"></div>

// in controller
$scope.init = function () {
    // check if there is query in url
    // and fire search in case its value is not empty
};

But take care about it as angular documentation implies (since v1.2) to NOT use ng-init for that. However imo it depends on architecture of your app.

I used ng-init when I wanted to pass a value from back-end into angular app:

<div data-ng-controller="myCtrl" data-ng-init="init('%some_backend_value%')"></div>